In medical practice, it is often necessary to administer medication either subcutaneously or intravenously under emergency conditions. For this purpose, pre-loaded, disposable medicinal syringes have heretofore been devised which permit the injection of a pre-measured medicinal or pharmaceutical dose. U.S. Pat. No. 4,410,323 issued Oct. 18, 1983 to HODASH, et al, describes a pre-dosed disposable syringe of this type wherein the medication is contained within a hollow, flexible member which acts as a syringe upon its manual compression for injection through the usual cannula. In such known pre-dosed disposable syringes, the resiliant container syringe member is of such thickness and rigidity that it cannot be fully collapsed about the inwardly-projecting end of the cannula, so as to provide for expression or injection of the entire dose. If the pre-measured dose to be injected is comparatively small, as may be the case in potent injectables, significant underdosing may result.